Condition-Based Method for Malfunction Prediction

ABSTRACT

To perform a prognostic health analysis for an asset, a plurality of independent stochastic simulations are performed using transition probabilities of a discrete Markov Chain model. A prognostic asset health state evolution is computed over a time horizon from the plurality of independent stochastic simulations. An output is generated based on the computed prognostic asset health state evolution.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/342,178, filed Jun. 6, 2021, which application claims the benefit ofEuropean Patent Application No. 20178839.5, filed on Jun. 8, 2020, whichapplications are hereby incorporated herein by reference.

TECHNICAL FIELD

The invention relates to techniques for assessing a health of an asset.The invention relates in particular to methods and devices for theprognostic assessment of asset health.

BACKGROUND

Electric power systems, such as power generation, transmission and/ordistribution system, and industrial systems include assets.Transformers, power generators, and distributed energy resource (DER)units are examples for such assets. The assets are subject todegradation during operation. For planning purposes, schedulingmaintenance or replacement work, it is desirable to estimate theremaining useful life (RUL) of assets.

RUL estimations may be based on sensor data for a fleet of assets of thesame or a similar type as the asset for which the RUL is to beestimated. The sensor data may be labeled with failure signatures,indicating whether the sensor data corresponds to normally operative,degraded, or failed states of an asset. As different types of sensordata may be available for different assets in the fleet, depending,e.g., on the manufacturer or on accessory sensors installed with theasset, it may be challenging to combine such sensor data for RULestimation.

Y. Yu et al., “Remaining Useful Life Prediction Using Elliptical BasisFunction Network and Markov Chain”, World Academy of Science,Engineering and Technology, 47, 2010 describes a method for remaininguseful life prediction using the Elliptical Basis Function (EBF) networkand a Markov chain. The EBF structure is trained by a modifiedExpectation-Maximization (EM) algorithm in order to take into accountthe missing covariate set. No explicit extrapolation is needed forinternal covariates while a Markov chain is constructed to represent theevolution of external covariates.

SUMMARY

Embodiments can provide enhanced techniques of predicting thetime-evolution of asset degradation. Particular embodiments providetechniques that allow the prognostic predictions to be made for adegradation of a health of an asset, without necessarily requiringsensor data captured for that specific asset for which the prediction isbeing made. Alternative or addition embodiments provide techniques thatcan use historical sensor data from a fleet of assets for making theprediction, even when different types of sensor data are available fordifferent assets in the fleet.

According to embodiments of the invention, methods and computing systems as recited in the independent claims are provided. The dependentclaims define preferred embodiments.

According to embodiments of the invention, a discrete Markov Chain modelmay be used to predict the performance degradation of an asset. A MarkovChain Monte Carlo (MCMC) method may be employed to perform a largenumber of simulations. The Markov Chain model may have a set of discretestates that correspond to different asset health states.

A potentially large volume of historical sensor data captured may becondensed into a small number of transition probabilities. Forillustration, the Markov Chain model may be set up in such a way thatonly two or three transition probabilities govern the transitionsbetween the states, which may be indicative of a healthy asset state, adegraded asset state in which the asset is still operative, and a failedasset state in which the asset has failed. The invention can also beapplied to cases in which little or no historical data is available. Thetransition probabilities of the Markov Chain model may then be set by ahuman expert.

Transition probabilities between the states of the Markov Chain modelmay be determined based on sensor data that are labeled with failuresignatures and that are captured on a fleet of assets.

Different transition probabilities may be used for simulations that arerun in parallel. The different transition probabilities may beassociated with different operating conditions and/or ambientconditions.

Information on a variance, confidence interval, or other reliabilityindicator may be determined from the simulations.

MCMC techniques that employ a small state space and a small number oftransition probabilities allow prognostic asset health analysis to beperformed over various time horizons, including time horizons that maybe several years or longer. Various other simulation approaches that aimat more detailed modeling of the asset behavior may be suitable forassessing asset degradation on shorter time scales, but may be subjectto instabilities over the longer time periods that are relevant forasset health analysis of electric power system assets or industrialassets.

A method of performing a prognostic health analysis for an asset, inparticular for determining a remaining useful life, RUL, or probabilityof failure (PoF) according to an embodiment comprises performing aplurality of independent stochastic simulations using transitionprobabilities of a discrete Markov Chain model. The discrete MarkovChain model has a state space that comprises a set of asset healthstates. Each of the plurality of independent stochastic simulationssimulates a future evolution in the state space of the discrete MarkovChain model over a prognostic horizon. The method may further comprisecomputing a prognostic asset health state evolution over the prognostichorizon from the plurality of independent stochastic simulations. Themethod may further comprise generating output based on the computedprognostic asset health state evolution.

The asset may be an electric power system asset or an industrial asset.

Computing the prognostic asset health state evolution may comprisecomputing a RUL.

Computing the prognostic asset health state evolution may comprisecomputing a probability of failure of the asset over the prognostichorizon as a function of time.

The method may further comprise computing confidence information for theprognostic asset health state evolution as a function of time over theprognostic horizon from the plurality of independent stochasticsimulations.

The output may further be generated based on the confidence information.

The confidence information may comprise a time evolution of a confidenceinterval over the prognostic horizon.

The method may further comprise computing variance information for theprognostic asset health state evolution as a function of time over theprognostic horizon from the plurality of independent stochasticsimulations.

The output may further be generated based on the variance information.

The variance information may comprise a time evolution of a varianceinterval over the prognostic horizon.

The confidence or variance information may comprise a time evolution ofa lower boundary and a time evolution of an upper boundary.

The lower boundary may be associated with a first set of transitionprobabilities and the upper boundary may be associated with a second setof transition probabilities different from the first set of transitionprobabilities.

The output may comprise a representation of the evolution of the assethealth state, an alarm or warning generated based on the evolution ofthe asset health state, and/or a control signal to control operation ofthe asset based on the evolution of the asset health state.

The method may comprise deriving the first set of transitionprobabilities from first sensor data of assets operating under firstconditions (e.g., first operating and/or ambient conditions) andderiving the second set of transition probabilities from second sensordata of assets operating under second conditions (e.g., second operatingand/or ambient conditions) different from the first operatingconditions.

The state space may consist of three states, four states, or more thanfour states.

The state space may comprise at least one state in which operation ofthe asset is not adversely affected by a failure.

The state space may comprise at least one state in which operation ofthe asset is adversely affected by a failure, but the asset continues tooperate.

The state space may comprise a state in which the asset is inoperativedue to a failure.

Computing the prognostic asset health state evolution may comprisecomputing, for a plurality of times within the prognostic horizon, aprobability distribution in the state space and mapping the probabilitydistribution to a scalar.

The scalar may be the probability for the asset to be in the state inwhich the asset is inoperative due to a failure, as determined by theplurality of independent simulations.

The prognostic asset health state evolution may be obtained as a timeevolution of the scalar.

The method may further comprise determining the transition probabilitiesfrom historical data comprising sensor data for a plurality of assets.

The sensor data may be labeled with failure signatures indicating atwhich time the respective asset was in which state of the state space ofthe Markov Chain model.

The failure signatures may be computed automatically or may be assignedbased on a received input from a human expert or may be assigned as acombination of both aforementioned approaches.

Determining the transition probabilities may comprise computing atime-dependent scalar function from the sensor data for the plurality ofassets.

The scalar function may be computed using heuristics that use sensormeasurements as inputs and output the scalar function.

Determining the transition probabilities may comprise identifyingtransitions within the state space of the Markov Chain model based onthe time-dependent scalar function.

Determining the transition probabilities may comprise computing thetransition probabilities based on the transitions within the state spaceof the Markov Chain model.

The determining step may comprise comparing the scalar function to oneor several thresholds.

The scalar function may be representative of a health index, indicatinga severity of degradation.

The determination of the transition probabilities may be performedindependently for different groups of sensor data, indicating differentoperating conditions and/or ambient conditions of the assets in thefleet.

The method may comprise determining plural sets of transitionprobabilities, each associated with for different operating conditionsand/or ambient conditions.

While plural sets of transition probabilities may be determined fordifferent operating conditions and/or ambient conditions, the statespace of the Markov Chain model may remain the same.

The method may comprise selecting one of the plural sets of transitionprobabilities for performing the simulations, depending on the operatingconditions and/or ambient conditions to which the asset is intended tobe subjected.

The method may comprise performing the plurality of independentstochastic simulations such that one or several first simulations areperformed using a first set of transition probabilities associated withfirst operating conditions and/or first ambient conditions, and one orseveral second simulations are performed using a second set oftransition probabilities associated with second operating conditionsand/or second ambient conditions, wherein the first transitionprobabilities are different from the second transition probabilities.

The different operating conditions may be indicative of different load,different voltage, different current, different operating points,different insulation fluid, without being limited thereto.

The different ambient conditions may be indicative of differenttemperature, different relative humidity, without being limited thereto.

The plurality of independent stochastic simulations may be Markov ChainMonte Carlo (MCMC) simulations.

The Markov Chain may be homogeneous. The transition probabilities may beindependent of time.

The Markov Chain may have order 1, i.e., transitions may be dependent onthe state in which the Markov Chain model is currently, while beingindependent of previous transitions to that state.

The Markov Chain model may be such that states have qualitativeinterpretation that is monotonically ordered, i.e., it is alwayspossible to compare two states in terms of severity of degradation.

Each state of the state space may have a non-zero transition probabilityto at most one other state of the state space, which describes moresevere degradation, and non-zero transition probability to itself.

The Markov Chain model may be such that states of the state space thatdo not correspond to failure of the asset have a non-zero transitionprobability to just one other state of the state space.

The Markov Chain model may be such that a state of the state space thatcorresponds to failure of the asset does not have any non-zerotransition probability to a state other than itself.

The Markov Chain model may be a finite Markov Chain model.

The state space may consist of three states, four states, or more thanfour states.

The state space may consist of n states where n is equal to three, four,or greater than four, wherein for n−1 states of the state space thatcorrespond to an operative asset the transition probability to only oneother state of the state space is non-zero, and for the state thatcorresponds to a failed asset there is no non-zero transitionprobability to any other state of the state space.

The method may further comprise receiving sensor measurement datacaptured during operation of the asset.

The method may further comprise updating the prognostic asset healthstate evolution based on the received sensor measurement data.

The plurality of simulations may comprise simulations for differentambient and/or operating scenarios.

The plurality of simulations may be performed in parallel.

The plurality of simulations may be performed concurrently.

The method may be a computer-implemented method.

The method may be performed by at least one integrated circuit.

The method may be performed by at least one integrated circuit of acentral controller of a decentralized control system.

The method may be performed by at least one integrated circuit of alocal controller of a decentralized control system.

The method may comprise receiving, by the at least one integratedcircuit, information on the transition probabilities over acommunication network.

The asset may be a power transformer, a distributed energy resource,DER, unit, or a power generator.

The prognostic horizon may be 1 year or more, 2 years or more, 3 yearsor more, 4 years or more, 5 years or more, 10 years or more, 15 years ormore, or 20 years or more.

The prognostic horizon may be 1 week or more, 1 month or more, etc.

The prognostic horizon may be measured in and may include a plurality ofcycles, e.g., a certain number of flight cycles, ship route cycles,train route cycles, etc.

A method of operating and/or maintaining an asset, comprises performinga prognostic asset health analysis for the asset using the methodaccording to an embodiment and automatically taking a control or outputaction based on the prognostic asset health analysis.

The control or output action may comprise performing at least one of thefollowing: generating an alarm or warning based on the computedprognostic asset health state evolution; generating a control signal tocontrol operation of the asset based on the computed prognostic assethealth state evolution; scheduling a down-time of the asset based on thecomputed prognostic asset health state evolution; scheduling maintenancework based on the computed prognostic asset health state evolution;scheduling replacement work based on the computed prognostic assethealth state evolution; changing maintenance intervals based on thecomputed prognostic asset health state evolution.

The control or output action may comprise outputting information on afailure probability as a function of operating time, on a scheduled orrescheduled maintenance work interval, or on a scheduled replacementwork interval via an interface.

A computing system operative to perform a prognostic health analysis foran asset according to the invention is configured to perform a pluralityof independent stochastic simulations using transition probabilities ofa discrete Markov Chain model, wherein the discrete Markov Chain modelhas a state space that comprises a set of asset health states andwherein each of the plurality of independent stochastic simulationssimulates a future evolution in the state space of the discrete MarkovChain model over a prognostic horizon. The computing system isconfigured to compute a prognostic asset health state evolution over theprognostic horizon from the plurality of independent stochasticsimulations. The computing system is configured to control generation ofoutput based on the computed prognostic asset health state evolution.

The computing system may include a local controller having one orseveral integrated circuit(s) operative to perform the independentstochastic simulations and compute the prognostic asset health stateevolution. The one or several IC(s) may be operative to perform theoperations described in detail herein.

The computing system may include a central controller having one orseveral integrated circuit(s) operative to perform the independentstochastic simulations and compute the prognostic asset health stateevolution. The one or several IC(s) may be operative to perform theoperations described in detail herein.

The asset may be an electric power system asset.

The asset may be an industrial asset.

The computing system may be operative such that computing the prognosticasset health state evolution may comprise computing a RUL

The computing system may be operative such that computing the prognosticasset health state evolution may comprise computing a probability offailure of the asset over the prognostic horizon as a function of time.

The computing system may be operative for computing confidenceinformation for the prognostic asset health state evolution as afunction of time over the prognostic horizon from the plurality ofindependent stochastic simulations.

The computing system may be operative such that the output may furtherbe generated based on the confidence information.

The computing system may be operative such that the confidenceinformation may comprise a time evolution of a confidence interval overthe prognostic horizon.

The computing system may be operative for computing variance informationfor the prognostic asset health state evolution as a function of timeover the prognostic horizon from the plurality of independent stochasticsimulations.

The computing system may be operative such that the output may furtherbe generated based on the variance information.

The computing system may be operative such that the output may comprisea representation of the evolution of the asset health state, an alarm orwarning generated based on the evolution of the asset health state,and/or a control signal to control operation of the asset based on theevolution of the asset health state.

The computing system may be operative such that the variance informationmay comprise a time evolution of a variance interval over the prognostichorizon.

The computing system may be operative such that the confidence orvariance information may comprise a time evolution of a lower boundaryand a time evolution of an upper boundary.

The computing system may be operative such that the lower boundary maybe associated with a first set of transition probabilities and the upperboundary may be associated with a second set of transition probabilitiesdifferent from the first set of transition probabilities.

The computing system may be operative for deriving the first set oftransition probabilities from first sensor data of assets operatingunder first conditions (e.g., first operating and/or ambient conditions)and deriving the second set of transition probabilities from secondsensor data of assets operating under second conditions (e.g., secondoperating and/or ambient conditions) different from the first operatingconditions.

The computing system may be operative such that the state space mayconsist of three states, four states, or more than four states.

The computing system may be operative such that the state space maycomprise at least one state in which operation of the asset is notadversely affected by a failure.

The computing system may be operative such that the state space maycomprise at least one state in which operation of the asset is adverselyaffected by a failure, but the asset continues to operate.

The computing system may be operative such that the state space maycomprise a state in which the asset is inoperative due to a failure.

The computing system may be operative such that computing the prognosticasset health state evolution may comprise computing, for a plurality oftimes within the prognostic horizon, a probability distribution in thestate space and mapping the probability distribution to a scalar.

The computing system may be operative such that the scalar may be theprobability for the asset to be in the state in which the asset isinoperative due to a failure, as determined by the plurality ofindependent simulations.

The computing system may be operative such that the prognostic assethealth state evolution may be obtained as a time evolution of thescalar.

The computing system may be operative for determining the transitionprobabilities from historical data comprising sensor data for aplurality of assets.

The computing system may be operative such that the sensor data may belabeled with failure signatures indicating at which time the respectiveasset was in which state of the state space of the Markov Chain model.

The computing system may be operative to automatically compute thefailure signatures or receive input from a human expert that is used fordetermining the failure signatures.

The computing system may be operative such that determining thetransition probabilities may comprise computing a time-dependent scalarfunction from the sensor data for the plurality of assets.

The computing system may be operative such that the scalar function maybe computed using heuristics that use sensor measurements as inputs andoutput the scalar function.

The computing system may be operative such that determining thetransition probabilities may comprise identifying transitions within thestate space of the Markov Chain model based on the time-dependent scalarfunction.

The computing system may be operative such that determining thetransition probabilities may comprise computing the transitionprobabilities based on the transitions within the state space of theMarkov Chain model.

The computing system may be operative such that determining thetransition probabilities may comprise comparing the scalar function toone or several thresholds.

The scalar function may be representative of a health index, indicatinga severity of degradation.

The computing system may be operative such that the determination of thetransition probabilities may be performed independently for differentgroups of sensor data, indicating different operating conditions and/orambient conditions of the assets in the fleet.

The computing system may be operative for determining plural sets oftransition probabilities, each associated with for different operatingconditions and/or ambient conditions.

While plural sets of transition probabilities may be determined fordifferent operating conditions and/or ambient conditions, the statespace of the Markov Chain model may remain the same.

The computing system may be operative for selecting one of the pluralsets of transition probabilities for performing the simulations,depending on the operating conditions and/or ambient conditions to whichthe asset is intended to be subjected.

The computing system may be operative for performing the plurality ofindependent stochastic simulations such that one or several firstsimulations are performed using a first set of transition probabilitiesassociated with first operating conditions and/or first ambientconditions, and one or several second simulations are performed using asecond set of transition probabilities associated with second operatingconditions and/or second ambient conditions, wherein the firsttransition probabilities are different from the second transitionprobabilities.

The computing system may be operative such that different operatingconditions may be indicative of different load, different voltage,different current, different operating points, and different insulationfluid, without being limited thereto.

The different ambient conditions may be indicative of differenttemperature, different relative humidity, without being limited thereto.

The computing system may be operative such that the plurality ofindependent stochastic simulations may be Markov Chain Monte Carlo(MCMC) simulations.

The computing system may be operative such that the Markov Chain may behomogeneous. The transition probabilities may be independent of time.

The computing system may be operative such that the Markov Chain mayhave order 1, i.e., transitions may be dependent on the state in whichthe Markov Chain model is currently, while being independent of previoustransitions to that state.

The computing system may be operative such that each state of the statespace may have a non-zero transition probability to at most one otherstate of the state space.

The computing system may be operative such that the Markov Chain modelmay be such that states of the state space that do not correspond tofailure of the asset have a non-zero transition probability to just oneother state of the state space.

The computing system may be operative such that the Markov Chain modelmay be such that a state of the state space that corresponds to failureof the asset does not have any non-zero transition probability to astate other than itself.

The computing system may be operative such that the Markov Chain modelis a finite Markov Chain model.

The computing system may be operative such that the state space mayconsist of four or three states.

The computing system may be operative such that the state space mayconsist of n states where n is equal to three, four, or greater thanfour, wherein for n−1 states of the state space that correspond to anoperative asset the transition probability to only one other state ofthe state space is non-zero, and for the state that corresponds to afailed asset there is no non-zero transition probability to any otherstate of the state space.

The computing system may be operative for receiving sensor measurementdata captured during operation of the asset.

The computing system may be operative for updating the prognostic assethealth state evolution based on the received sensor measurement data.

The computing system may be operative such that the plurality ofsimulations may comprise simulations for different ambient and/oroperating scenarios.

The computing system may be operative such that the plurality ofsimulations are performed in parallel.

The computing system may be operative such that the plurality ofsimulations are performed concurrently.

The computing system has at least one integrated circuit to perform therecited operations. The recited operations may be performed in adistributed computing system, e.g., in a decentralized control systemand/or using a cloud-based computing system.

The computing system may have an interface to receive information on thetransition probabilities over a communication network.

The asset may be a power transformer, a distributed energy resource,DER, unit, or a power generator.

The prognostic horizon may be 1 year or more, 2 years or more, 3 yearsor more, 4 years or more, 5 years or more, 10 years or more, 15 years ormore, or 20 years or more.

The prognostic horizon may be 1 week or more, 1 month or more, etc.

The prognostic horizon may be measured in and may include a plurality ofcycles, e.g., a certain number of flight cycles, ship route cycles,train route cycles, etc.

A control system for an asset comprises the computing system forperforming a prognostic asset health analysis for the asset using themethod according to an embodiment and an output interface toautomatically trigger or effect a control or output action based on theprognostic asset health analysis.

The control or output action may comprise performing at least one of thefollowing: generating an alarm or warning based on the computedprognostic asset health state evolution; generating a control signal tocontrol operation of the asset based on the computed prognostic assethealth state evolution; scheduling a down-time of the asset based on thecomputed prognostic asset health state evolution; scheduling maintenancework based on the computed prognostic asset health state evolution;scheduling replacement work based on the computed prognostic assethealth state evolution; changing maintenance intervals based on thecomputed prognostic asset health state evolution.

The control or output action may comprise outputting information on afailure probability as a function of operating time, on a scheduled orrescheduled maintenance work interval, or on a scheduled replacementwork interval via an interface.

An industrial or power system, comprises an asset and the computingsystem to perform a prognostic asset health analysis for the asset.

The computing system may be a decentralized controller of the industrialor power system for controlling the asset.

Various effects and advantages are associated with the invention. Whenusing a Markov Chain model with a discrete state space and non-zerotransition probabilities to at most one other state of the Markov Chainmodel that corresponds to the next degree of severity of degradation,only a small number of parameters is requires. This is particularly thecase when the Markov Chain model has a state space that may consist of arather small number of states (e.g., three or four states, butoptionally also a larger number of states), where only a small number oftransition probabilities between the states is required for carrying outthe method. The transition probabilities may be set based on a userinput or may be determined automatically from sensor data with failuresignatures, even when different types of sensor data are available fordifferent assets in the fleet.

RUL curves or other prognostic asset health information may bedetermined starting from sensor data of arbitrary dimension based on theMarkov Chain model, using stochastic simulation techniques.

The distribution of RUL curves or other prognostic asset healthinformation may be determined based on the stochastic simulations fordifferent ambient and/or operating conditions. This allows quantitativeinformation to be provided not only for the expected RUL curve, but alsoits confidence interval. Precision and/or variance of the RULdistribution can be quantified and output.

By integrating multiple stochastic simulations into a simulation stepthat allows the stochastic simulations to be executed in parallel, highspeed of computation may be attained.

Additional information can be generated, such as quantitativeinformation on a variance or confidence interval of a RUL curve, whichcan be used in prescriptive tools or applications.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject-matter of the invention will be explained in more detailwith reference to preferred exemplary embodiments which are illustratedin the attached drawings, in which:

FIG. 1 is a schematic view of a power system having a computing systemaccording to an embodiment.

FIG. 2 is a schematic view of a power system having a computing systemaccording to an embodiment.

FIG. 3 is a diagram representing a Markov Chain model employed inembodiments.

FIG. 4 is a flow chart of a method according to an embodiment.

FIG. 5 is a graph illustrating exemplary output generated by a methodand computing system according to an embodiment.

FIG. 6 are bar diagrams illustrating a time evolution of stateoccupation probabilities.

FIG. 7 is a graph illustrating exemplary output generated by a methodand computing system according to an embodiment.

FIGS. 8A and 8B are graphs illustrating results of a prognostic assethealth state analysis in combination with observed asset health states.

FIG. 9 is a flow chart of a method according to an embodiment.

FIG. 10 is a block diagram of a computing system according to anembodiment.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Exemplary embodiments of the invention will be described with referenceto the drawings in which identical or similar reference signs designateidentical or similar elements. While some embodiments will be describedin the context of assets of a power system, such as distributed energyresource (DER) units or transformers, the embodiments are not limitedthereto. The features of embodiments may be combined with each other,unless specifically noted otherwise.

FIGS. 1 and 2 are schematic views of a power system 10, 15. The powersystems 10, 15 comprise a plurality of assets. The assets may includegenerators, such as distributed energy resource (DER) units 11-13,16-18, transformers, or other electric power system assets.

The power system 10, 15 includes a control system comprising localcontrollers 21-23, each associated with an asset. The control system mayinclude a central system 20. The central system 20 may becommunicatively coupled with the local controllers. The central system20 may be communicatively coupled with a remote (e.g., cloud-based)server system 24.

As will be described in more detail below, the local controllers 21-23,the central system 20, and/or the remote server system 24 may beoperative to perform a prognostic asset health analysis, using a MarkovChain model. The Markov Chain model may have a specific configuration,as will be explained below. The local controllers 21-23, the centralsystem 20, and/or the remote server system 24 may be operative toperform a plurality of independent stochastic simulations, in particulara Markov Chain Monte Carlo (MCMC) simulation, to perform the prognosticasset health analysis.

Results of the prognostic asset health analysis may be used by the localcontrollers 21-23, the central system 20, and/or the remote serversystem 24 for scheduling down-times, maintenance work, replacement workor for automatically performing control operations. The localcontrollers 21-23, the central system 20, and/or the remote serversystem 24 may be operative to generate and output control or outputdata. Output may be provided via a human machine interface (HMI) 26. TheHMI may be coupled to the local controllers 21-23, the central system20, and/or the remote server system 24 via the internet or another widearea network (WAN).

As will be explained in more detail with reference to FIG. 3 to FIG. 10, the prognostic asset health analysis may involve simulatingtime-evolution of an asset. The MCMC simulations and further processingof the MCMC results may be performed at the local controllers 21-23.This facilitates the incorporation of local sensor measurements forupdating the prognostic asset health analysis.

The techniques described herein may also be used when no sensor data areavailable for the specific asset for which the prognostic asset healthanalysis is performed. For illustration, a remaining useful life (RUL)curve or other prognostic asset health prediction may be computed forassets even when no sensor data is (yet) available, using a historicaldata repository that includes sensor data and information on failurescaptured for similar assets, preferably for assets of the same type asthe asset for which the prognostic asset health analysis is performed.

FIG. 3 is a graph of a Markov Chain model that can be used in methodsand computing systems according to embodiments. A state space of theMarkov Chain model consists of a set of n states S1, . . . , Sn. In thepresent case, n=4. However, a state space having a different number ofstates (e.g., n=3 or n=5 or n>5) may be used instead.

The states of the state space may be ordered in such a manner that aseverity of degradation of the asset health increases from S1 to S2,from S2 to S3, etc., i.e., all but the last state of the Markov Chainmodel may be followed by another state that represents a more severedegradation. The last state of the Markov Chain model may represent themost severe degradation.

The Markov Chain model may be set up in such a way that the 1^(st),2^(nd), . . . (n−1)^(th) state 41-43 have a non-zero transitionprobability p₁₂, p₂₃, p₃₄ to just one other state of the state space.The n^(th) state 44 does not have a non-zero transition probability to astate other than itself.

For illustration, the Markov Chain model may be such that there is afinite transition probability p₁₂ from the first state 41 to the secondstate 42, but a zero transition probability from the second state 42back to the first state 41. With probability 1−p₁₂, the first state 41is maintained in an iteration of the stochastic simulation.

The Markov Chain model may be such that there is a finite transitionprobability p₂ from the second state 42 to the third state 43, but azero transition probability from the third state 43 back to the secondstate 42. With probability 1−p₂₃, the second state 42 is maintained inan iteration of the stochastic simulation.

The Markov Chain model may be such that there is a finite transitionprobability p₃₄ from the third state 43 to the fourth state 44, but azero transition probability from the fourth state 44 back to the thirdstate 43. With probability 1−p₃₄, the third state 43 is maintained in aniteration of the stochastic simulation.

The final state 44 of the Markov Chain model may correspond to a statein which the asset has failed to such a degree that it is no longeroperative.

The other states 41-43 of the state space may correspond to differentdegrees of degradation.

For illustration, a first state 41 (which may also be referred to as“unknown” state S1) may correspond to an asset state in which there isno known degradation that would affect asset operation. Forillustration, the first state 41 may correspond to a state in which nofailures are recorded or in which no failures can be recorded.

A second state 42 (which may also be referred to as “incipient” stateS2) may correspond to a detectable failure that are of such minorseverity that they do not immediately affect the asset's performance.Such incipient failures are usually characterized by short Mean Time toRepair (MTTR), low repair costs, and low impact on overall performance.If not maintained properly, the incipient failures can evolve into moresevere degraded failures.

A third state 43 (which may also be referred to as “degraded” state S3)may correspond to a mode that describes failures that significantlyreduce the system's performance but do not lead to immediate assetshutdown. Usually such failures are caused by components deterioration.If left untreated, the degraded will eventually lead to the criticalfailure.

The fourth state 44 (which may also be referred to as “critical” stateS4) may correspond to the most severe failure mode that causes animmediate and complete shutdown of the asset. It is usuallycharacterized by long and costly (due to complete production loss) MTTR.

The transition probabilities of the Markov Chain model may be receivedvia a user interface from a human expert or may be determined usinghistorical data, as will be described below. Various sets of transitionprobabilities p₁₂, p₂₃, p₃₄ may be used. For illustration, N>1, inparticular N>2 different sets of transition probabilities p₁₂, p₂₃, p₃₄may be used to simulate the evolution of the asset health state underdifferent ambient and/or operating conditions.

FIG. 4 is a flow chart of a method 50 according to an embodiment. Themethod 50 may be performed automatically by one or several IC(s) in thelocal controllers 21-23, the central system 20, and/or the remote serversystem 24.

At step 51, MCMC simulations or other stochastic simulations of theMarkov Chain model are performed. Step 51 may include performing morethan 100, more than 1000, more than 2000, more than 5000 simulations,more than 10000 simulations, more than 50000 simulations, more than100000 simulations, more than 500000 simulations, or one million or moresimulations. With increasing computational power, there is no upperbound for the number of simulations. The simulations may be performed inparallel.

While a large number of simulations (e.g., more than 100 or more than1000) may be performed for any set of transition probabilities p₁₂, p₂₃,p₃₄ of the Markov Chain model, the transition probabilities need not bethe same for all simulations. Different sets of transition probabilitiesp₁₂, p₂₃, p₃₄ may be used to quantitatively assess the impact ofdifferent operating conditions and/or ambient conditions.

The simulations may be performed over a time horizon. The time horizonmay be dependent on the specific asset. For power system assets such astransformers, typical lifetimes are in excess of 10 years, in excess of20 years, or even longer. Thus, the stochastic simulations may beperformed over time horizons that are in excess of 10 years, in excessof 20 years, or even longer. The time horizons may also be shorter,depending on the asset. For illustration, the prognostic time horizonmay be 1 week or more, 1 month or more, etc. The prognostic time horizonmay be measured in and may include a plurality of cycles, e.g., acertain number of flight cycles, ship route cycles, train route cycles,etc.

An initial state for the simulations may be selected depending oninformation on the asset is available. If no information on the asset isavailable, the simulations may all start with the first state 41 inwhich there is no information on detectable failures. If information onthe asset is available, e.g. sensor data collected after installation,this sensor data may be used for initializing the simulations. Adistribution of initial states for the various MCMC or other stochasticsimulations may be selected depending on whether the already collectedsensor data indicates that there is no recognizable failure that affectsasset performance or whether there are detectable issues that affectasset performance.

Furthermore, the initialization can be probabilistic. For illustration,if the information available is not conclusive whether the asset is instate 41 or 42 with equal chances to be in either of these states, thesystem can be initialized with a Bayesian prior distribution such thatprobability of the asset being in state 41 equals to 50% and probabilityof the asset being in state 42 equals to 50%. Other probabilisticinitiations with more states and different probabilities may also bepossible.

At step 52, the results of the stochastic simulations are processed.This may comprise computing a probability, as a function of time overthe time horizon, that the Markov Chain model has evolved into thecritical state that corresponds to an inoperative asset. The processingat step 53 may comprise computing a time evolution of a health indexthat, for any time during the prognostic time horizon, depends on theprobabilities for the Markov Chain model to be in the 1^(st), 2^(nd), .. . n^(th) state 41-44 of the Markov Chain model. The processing maycomprise computing a RUL curve or another output that indicates aprobability of asset failure as a function of operating time.

At step 53, output may be generated. The output may include informationon the asset's remaining useful life as a function of time. The outputmay include information on the asset's probability of failure as afunction of time. The output may include control and/or output data thatis obtained by further processing of the simulations results, such as aschedule for inspection, maintenance or replacement work on the asset.

FIG. 5 is a schematic view of an output 60 that may be automaticallygenerated and output. The output 60 may indicate the probability thatthe Markov Chain model has evolved into the critical state thatcorresponds to an inoperative asset. The output 60 may be determined bycomputing, for each one of a plurality of times over the time horizon,the fraction of simulations in which the Markov Chain model is in thecritical state S4 of the state space.

Additional or alternative output may be generated. For illustration, aRUL curve or other information indicative of the asset's degradation maybe processed to automatically schedule inspection, maintenance, orreplacement work, to output the schedule information to an operatorand/or to automatically schedule down-times.

Alternatively or additionally, the RUL curve or other informationindicative of the asset's degradation may be processed, using thresholdcomparisons or other triggers, to determine whether and when alarms,warnings, or other signals are to be output to the operator.

FIG. 6 illustrates the stochastic distribution 61-64 of the populationof the various states S1-S4 of the state space of the Markov Chainmodel. The distribution 61 corresponds to a first time in which most ofthe Markov Chain model simulations are still in the state S1 thatcorresponds to an asset with no detectable degradation. Thedistributions 62, 63 correspond to later second and third times in whichthe states S2 and S3 that correspond to incipient or more advanceddegradation have become more populated. The distribution 64 correspondsto an even later fourth time at which the critical state S4corresponding to asset shutdown is populated most, reflecting that it ismore probable for the asset to be in the inoperative state by that timethan in an operative state.

While relevant prognostic asset health predictions may be obtained fromthe probability for the asset to be in the critical state S4, which isthe final state of the Markov Chain model, the output into which theresults of the stochastic simulations are processed may depend on allprobabilities p₁, p₂, . . . p_(n) for the Markov Chain model to be inthe respective 1^(st), 2^(nd), . . . n^(th) state, as determined by thestochastic simulations.

For illustration, for any time j within the time horizon over which thestochastic simulations are performed, a scalar function

d(j)=Σ_(i=1, . . . ,n) p _(i)(j)×m _(i)  (1)

may be computed, where p_(i)(j) designates the probability for theMarkov Chain model to be in the i^(th) state at time j, as determined bythe stochastic simulations, and where m_(i) denotes a scalar value thatis a monotonous, in particular strictly monotonous, function of statelabel i. For illustration, all m_(i) may be selected from an intervalsuch that m₁≤m₂≤ . . . ≤m_(n), in particular such that m₁<m₂< . . .<m_(n).

By outputting the function d(j) or information derived therefrom, adegradation that results in reduced RUL may be reflected more adequatelyeven if it has not yet resulted in the asset reaching the critical stateS4.

The function d(j) is indicative of a degradation and can be related to ahealth index h(j) by h(j)=1−d(j), when d(j) is constrained to takevalues between 0 and 1.

FIG. 7 illustrates an output of a curve 80 that is indicative of theasset's degradation as a function of time as determined by thestochastic simulations. The curve 80 may be dependent on the timeevolution of all probabilities p₁, p₂, . . . p_(n) for the Markov Chainmodel to be in the respective 1^(st), 2^(nd), . . . n^(th) state, asdetermined by the stochastic simulations.

The various states of the Markov Chain model may be associated with aplurality of intervals 71-74. For illustration, for a health index hwithin interval 71, the asset may be determined to be in the state S1 inwhich there is no known degradation. For a health index h withininterval 72, the asset may be determined to be in the state S2 in whichthere is no incipient degradation that does not affect the performance.For a health index h within interval 73, the asset may be determined tobe in the state S3 in which there is a more severe degradation thataffects the performance, but does not lead to immediate asset shutdown.For a health index h within interval 74, the asset may be determined tobe in the state S4 in which the state is critical, leading to immediateasset shutdown.

Thresholds TH₁, . . . TH_(n-1) may define the upper and lower boundariesof the intervals 71-74. Comparisons to threshold TH₁, . . . TH_(n-1) maybe used when initializing the stochastic simulations for an asset. Forillustration, available sensor data for the asset may be processed intoa scalar representing the asset's health index h or degradation indexd=1−h, and the scalar may be compared to the thresholds TH₁, . . .TH_(n-1) to determine how the simulations are to be initialized.

By performing stochastic simulations such as MCMC, not only theevolution of the asset's health state, but also the reliabilityassociated with the determined evolution may be automatically determinedand output.

The information on the reliability may take various forms. Forillustration, an evolution of a confidence interval around the curves60, 80 may be determined as a function of time over the prognostic timehorizon. The time evolution of the confidence interval may indicate, forany time j of the prognostic time horizon, a lower boundary and an upperboundary for the critical failure probability 60 or for a health indexh. The upper and lower boundaries may be determined such that at least acertain percentage (e.g., at least 70%, 80%, 90%, or 95%) of thestochastic simulations gives rise to a critical failure probability 60or a health index h within the range between the upper and lowerboundaries. Exemplary upper and lower boundaries 81, 82 indicating thetime evolution of the confidence interval are shown in FIG. 7 .

Alternatively or additionally, the upper and lower boundaries 81, 82 mayreflect the variance in operating and/or ambient conditions to which theasset may be subjected. For illustration, the curves 80, 81, and 82 mayeach be obtained by performing plural stochastic simulations using aMarkov Chain model as explained with reference to FIG. 3 , but withdifferent sets of transitions probabilities.

FIGS. 8A and 8B show the time-evolution of a health index 80 determinedfrom the stochastic simulations and of upper and lower boundaries 81, 82indicating the time evolution of the confidence interval. The curves80-82 have been obtained by MCMC using transition probabilitiesdetermined from historical sensor data with associated failuresignatures, allowing transitions between the states S1-S4 to beidentified in the historical sensor data.

The curves 84, 86 represent the observed actual degradation of assets ofthe same asset type, but not included in the historical data used fordetermining the transition probabilities of the Markov Chain model. Thedegradation is indicated as evolution of a continuous function, which isa degradation index. Different states of the Markov Chain model may beassociated with various ranges of the degradation index function.

The prognostic asset health analysis results 80-82 are stochasticresults. While the actual state of an asset 84, 86 may also evolvedifferently than predicted by the curve 8 o and/or the confidenceinterval evolution 81, 82, the prognostic asset health analysis results80-82 reliably indicate the evolution of the asset degradation asdetermined on a large stochastic sample of assets.

FIG. 9 is a flow chart of a method go according to an embodiment. Themethod 90 may be performed automatically by the local controllers 21-23,the central system 20, and/or the remote server system 24. In oneimplementation, steps 91-92 of the method may be performed by centralsystem or remote server system 24, while steps 93-94 may be performed bylocal controllers 21-23. In other variants, the steps 91-94 may beotherwise distributed over plural IC(s) of a processing system.

At step 91, sensor data is received. The sensor data may be historicalsensor data of assets of the same asset type (e.g., photovoltaic panelwith a certain power rating range; wind turbine generator with a certainpower rating range; transformer of a rating in a certain interval) asthe asset(s) for which the prognostic asset health analysis is to beperformed.

The sensor data may be associated with a time period that exceed theprognostic time horizon in duration.

The sensor data may be labeled sensor data that includes information onstates, e.g. on states S1-Sn. For illustration, for any set of sensordata, there may be information that associates the sensor data with oneof the states S1, . . . , Sn of the Markov Chain model.

If the sensor data does not include the failure signatures, step 91 mayinclude receiving, via a user interface, information from a human expertassigning the sensor data to the states S1, . . . , Sn of the MarkovChain model.

If the sensor data does not include the failure signatures, step 91 mayinclude computing a scalar function from the sensor data, which isrepresentative of the degradation or health index of the respectiveasset in the fleet, and comparing the scalar function to one or severalthresholds (such as the thresholds TH1-TH3 in FIG. 7 ) to determine thetimes at which transitions between the S1, . . . , Sn have taken placebased on the sensor data.

The scalar function may be computed from sensor measurements usingheuristics.

The scalar function may take sensor measurements captured at varioustimes as inputs and may process them into a scalar function thatrepresents the observed evolution of asset health, as reflected by thehealth index h or degradation index d.

Various techniques may be used to compute the scalar function that isused to identify transitions between the discrete states. Forillustration, sensor measurements may be compared to a range ofoperation values. For each sensor measurement outside the range, apenalty may be imposed. Weighted summation or other processing thatcombines products of a weighting factor for a sensor measurement and avalue that depends on the deviation of the sensor measurement from thenormal operation value range may be used. The weighting factors aredependent on the respective sensor and indicate the importance of themeasurement for asset health.

Tools are known that provide a mapping of sensor measurements into acontinuous health or degradation functions for a wide variety of assets,including, without limitation, circuit-breakers, batteries (such asLi-ion batteries), or transformers. For illustration, tools such as theEllipse APM or RelCare tool process sensor measurements to provide afunction having a value in a continuous range and indicating the assethealth. Normalization may be used to normalize the health or degradationfunction to a desired range (such as from 0 to 1).

The techniques disclosed herein allow any health or degradation functionto be mapped to the discrete states of the state model, using optionalnormalization and a threshold comparison.

At step 92, transition probabilities of the Markov Chain model may bedetermined. The transition probabilities may be determined automaticallyfrom the sensor data and the associated state labels.

In an exemplary implementation, the transition probabilities may bedetermined based on conditional probabilities. For illustration, thetransition probability at a time j for a transition from the i^(th)state to the (i+1)^(th) state (where 1≤i≤n−1) may be determined as

p _(i→i+1)(j)=#(x _(j+1) =S _(i+1) ∧x _(j) =S _(i))/#(x _(j) =S_(i)).  (2)

In Equation (2), the numerator represents the number of assets whichwere in the i^(th) state at time j and transitioned to the (i+1)^(th)state at time j+1. The denominator represents the number of assets whichwere in the i^(th) state at time j.

The transition probabilities may be set and/or adjusted based on a userinput. Averaging or other processing may be performed to obtain theprobabilities of a homogeneous Markov Chain model.

When sensor data are available for different groups of assets that havethe same asset type (e.g., photovoltaic panel with a certain powerrating range; wind turbine generator with a certain power rating range;transformer of a rating in a certain interval), but which were subjectedto different operating conditions and/or ambient conditions, thetransition probabilities may be determined independently for each of thegroups.

At step 93, the transition probabilities may be used to perform a RULcomputation or to otherwise determine the time evolution of thedegradation of one or several assets. This may involve MCMC simulations,followed by processing the results of the MCMC simulations to determinethe RUL curve or another indicator for the time-dependent degradation ofone or several assets.

Step 93 may comprise receiving, during operation of the asset, sensordata captured for the asset, and adapting the RUL computation based onthe sensor data as they become available. This may comprise updating theMCMC simulations based on the sensor data as they become available.

At step 94, a control and/or output operation may be automaticallyperformed based on the results of the RUL computation or otherprognostic asset health analysis.

For illustration, the RUL curve may be output. Information on atime-evolution of a confidence interval or variance may be concurrentlyoutput.

Alternatively or additionally, an operating point of the asset may beautomatically adjusted by the local controller 21-23 associated with theasset.

Alternatively or additionally, inspection, maintenance, and/orreplacement work may be automatically scheduled.

Alternatively or additionally, down-times for inspection, maintenance,and/or replacement work may be automatically scheduled.

Alternatively or additionally, alarms, warnings, or other output may begenerated for outputting via an HMI depending on the RUL curve or otherprognostic asset health state evolution.

FIG. 10 is a schematic diagram of a computing system 100. The computingsystem 100 may comprise one or several IC(s) 103. The IC(s) may includean application specific integrated circuits (ASIC), processor,controller, field programmable gate array (FGPA), or a combination ofplural such integrated circuits.

The IC(s) 103 may reside in the central system 20, one of the localcontrollers 21-23, the server system 24, or may be distributed acrossthese entities.

The IC(s) 103 may be operative to execute a stochastic simulation engine104 to simulate the future evolution of an asset using a Markov Chainmodel. The stochastic simulation engine 104 may be adapted to performMCMC simulations.

The transition probabilities for the Markov Chain model used by thestochastic simulation engine 104 may be received via an interface 101(e.g., when the IC(s) 103 are resident in one of the local controllers21-23 and the central system 20 computes the transition probabilities).The transition probabilities may be computed by the IC(s) 103 based onhistorical sensor data for a fleet of assets having the same asset typeas the asset for which the prognostic asset health analysis is to beperformed. The historical sensor data may be received via the interface101 or may be stored locally in a data storage device 102.

The IC(s) 103 may be operative to execute a prediction engine 105. Theprediction engine 105 may compute a RUL curve or other prognosticinformation associated with an asset health state evolution based on theresults of the simulations performed by the stochastic simulation engine104.

The IC(s) 103 may be operative to execute an output engine 106. Theoutput engine 106 may generate output data or output signals forcontrolling an HMI and/or implementing a control operation for the assetor the system in which the asset is being used. For illustration, theoutput engine 106 may be operative to generate and output data to an HMIsuch that a RUL curve is output. The output engine 106 may be operativeto generate and output data to the HMI such that information on atime-evolution of a confidence interval or variance may be concurrentlyoutput.

Alternatively or additionally, the output engine 106 may be operative toautomatically adjust an operating point of the asset in response to theoutput of the prediction engine 105.

Alternatively or additionally, the output engine 106 may be operative toautomatically generate and output information on inspection,maintenance, and/or replacement work.

Alternatively or additionally, the output engine 106 may be operative toautomatically generate and output information on down-times forinspection, maintenance, and/or replacement work may be automaticallyscheduled.

Alternatively or additionally, the output engine 106 may be operative toautomatically generate and output alarms, warnings, or other output maybe generated for outputting via an HMI depending on the RUL curve orother prognostic asset health state evolution.

Various effects and advantages are associated with the invention. Byusing a Markov Chain model with a state space that may consist of arather small number of states (e.g., three or four states), only a smallnumber of transition probabilities between the states is required forcarrying out the method. RUL curves or other prognostic asset healthinformation may be determined efficiently. Quantitative information maybe provided not only for the expected RUL curve, but also its confidenceinterval. Precision and/or variance information can be quantified andoutput.

The methods and systems according to the invention may be used inassociation with electric power system assets, such as assets of powergeneration, distribution and/or transmission systems, or assets ofindustrial systems, without being limited thereto.

While the invention has been described in detail in the drawings andforegoing description, such description is to be considered illustrativeor exemplary and not restrictive. Variations to the disclosedembodiments can be understood and effected by those skilled in the artand practicing the claimed invention, from a study of the drawings, thedisclosure, and the appended claims. In the claims, the word“comprising” does not exclude other elements or steps, and theindefinite article “a” or “an” does not exclude a plurality. The merefact that certain elements or steps are recited in distinct claims doesnot indicate that a combination of these elements or steps cannot beused to advantage, specifically, in addition to the actual claimdependency, any further meaningful claim combination shall be considereddisclosed.

1. A method of performing a prognostic health analysis for an asset, themethod comprising: performing a plurality of independent stochasticsimulations using transition probabilities of a discrete Markov Chainmodel, wherein the discrete Markov Chain model has a state space thatcomprises a set of asset health states and wherein each of the pluralityof independent stochastic simulations simulates a future evolution inthe state space of the discrete Markov Chain model over a prognostichorizon; computing a prognostic asset health state evolution over theprognostic horizon from the plurality of independent stochasticsimulations, wherein computing the prognostic asset health stateevolution comprises computing a time-dependent scalar function based onprobabilities that the discrete Markov Chain model is in a particularstate at a particular time as determined from each of the plurality ofindependent stochastic simulations; generating output based on thecomputed prognostic asset health state evolution; and automaticallyperforming an action relating to the asset based on the computedprognostic asset health state evolution.
 2. The method of claim 1,wherein the asset is a power system asset or an industrial asset.
 3. Themethod of claim 1, wherein generating the output comprises generating anoutput related to a remaining useful life (RUL) or a probability offailure (PoF).
 4. The method of claim 1, wherein computing theprognostic asset health state evolution comprises computing a remaininguseful life.
 5. The method of claim 1, further comprising computingconfidence or variance information for the prognostic asset health stateevolution as a function of time over the prognostic horizon from theplurality of independent stochastic simulations, wherein the output isfurther generated based on the confidence or variance information. 6.The method of claim 5, wherein the output is further generated based onthe confidence information and wherein the confidence informationcomprises a future evolution of a confidence interval over theprognostic horizon.
 7. The method of claim 5, wherein the output isfurther generated based on the variance information and wherein thevariance information comprises a future evolution of a variance over theprognostic horizon.
 8. The method of claim 5, wherein the confidence orvariance information comprises a time evolution of a lower boundary anda time evolution of an upper boundary, the lower boundary beingassociated with a first set of transition probabilities and the upperboundary being associated with a second set of transition probabilitiesdifferent from the first set of transition probabilities.
 9. The methodof claim 1, wherein the state space comprises: at least one state inwhich operation of the asset is not adversely affected by a failure; atleast one state in which operation of the asset is adversely affected bya failure, but the asset continues to operate; and a state in which theasset is inoperative due to a failure.
 10. The method of claim 1,wherein computing the prognostic asset health state evolution comprisescomputing, for a plurality of times within the prognostic horizon, aprobability distribution in the state space and mapping the probabilitydistribution to a scalar.
 11. The method of claim 10, wherein theprognostic asset health state evolution is obtained as a time evolutionof the scalar.
 12. The method of claim 1, further comprising determiningthe transition probabilities from historical data comprising sensor datafor a plurality of assets.
 13. The method of claim 12, whereindetermining the transition probabilities comprises: computing thetime-dependent scalar function from sensor data for the plurality ofassets, identifying transitions within the state space of the discreteMarkov Chain model based on the time-dependent scalar function, andcomputing the transition probabilities based on the transitions withinthe state space of the discrete Markov Chain model.
 14. The method ofclaim 1, wherein the plurality of independent stochastic simulations areMarkov Chain Monte Carlo simulations.
 15. The method of claim 1, furthercomprising: receiving sensor measurement data captured during operationof the asset; and updating the prognostic asset health state evolutionbased on the received sensor measurement data.
 16. The method of claim1, wherein the plurality of simulations comprise simulations fordifferent ambient or operating scenarios.
 17. The method of claim 1,wherein: the asset is a power transformer, a distributed energyresource, DER, unit, or a power generator; or the prognostic horizon is1 year or more.
 18. A method of performing a prognostic health analysisfor an asset, the method comprising: performing a plurality ofindependent stochastic simulations using transition probabilities of adiscrete Markov Chain model, wherein the discrete Markov Chain model hasa state space that comprises a set of asset health states and whereineach of the plurality of independent stochastic simulations simulates afuture evolution in the state space of the discrete Markov Chain modelover a prognostic horizon; computing a prognostic asset health stateevolution over the prognostic horizon from the plurality of independentstochastic simulations, wherein computing the prognostic asset healthstate evolution comprises computing a function based on probabilitiesthat the discrete Markov Chain model are in particular states during theprognostic horizon as determined from each of the plurality ofindependent stochastic simulations; generating output based on thecomputed prognostic asset health state evolution; and automaticallyperforming an action relating to the asset based on the computedprognostic asset health state evolution.
 19. The method of claim 18,wherein the prognostic horizon is at least one year.
 20. Anon-transitory computer readable medium with instructions storedthereon, wherein, when executed by a processor, the instructions enablethe processor to: perform a plurality of independent stochasticsimulations using transition probabilities of a discrete Markov Chainmodel, wherein the discrete Markov Chain model has a state space thatcomprises a set of asset health states and wherein each of the pluralityof independent stochastic simulations simulates a future evolution inthe state space of the discrete Markov Chain model over a prognostichorizon; compute a prognostic asset health state evolution over theprognostic horizon from the plurality of independent stochasticsimulations, wherein computing the prognostic asset health stateevolution comprises computing a function based on probabilities that thediscrete Markov Chain model are in particular states during theprognostic horizon as determined from each of the plurality ofindependent stochastic simulations; generate output based on thecomputed prognostic asset health state evolution; and automaticallyperform an action relating to the asset based on the computed prognosticasset health state evolution.